Document Type

Post-Print

Publication Date

6-2002

Abstract

In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k>2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu's conjecture but the question on the structure of the boundary of the basins of attraction of the locally stable n-cycles is still open.

Document Object Identifier (DOI)

10.1080/10236190290027666

Publication Information

Journal of Difference Equations and Applications

Included in

Mathematics Commons

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